Update: after much searching on the Kodak website, I found, in the "Extended User's Guide" some information I was looking for. To shoot videos without holding the button down, press and release the button to start shooting, then, press and release again to stop shooting.
Apparently the "press and hold" method I had been using is an undocumented feature of the camera -- I don't see it mentioned in the literature. To use it, press and hold -- the camera will begin capturing video. When you release the button, the camera will stop recording video. There must be some cutoff point between the documented press-and-release timeframe and the press-and-hold system, but so far, it seems to be fairly intuitive, so I assume that the camera waits a fairly short amount of time for the release (to decide if you're doing a press-release...shoot...press-release...stop, or press...shoot...release...stop video).
I still haven't been able to find any info on the availability of a cable release (electronic, presumably) for this camera, but I did find an ebay seller who is pitching replacement USB cables for it at a reasonable price (four bucks and change, free shipping, versus Kodak charging something like $25 plus freight). I plan on getting a couple of spares. Also need to find an A/V cable, to make it easy to copy videos to a VCR or DVD recorder.